The price of a certain television set is discounted by 10% and the reduced prce is then discounted by 10%. This series of successive discounts is equivalent to a single discount of

Options

A. `20%`
B. `19%`
C. `18%`
D. `11%`

Answer

To find the equivalent single discount for two successive discounts of 10%, we can use the formula for successive discounts:

\[ \text{Single Equivalent Discount} = x + y - \frac{xy}{100} \]

where \( x \) and \( y \) are the percentages of the two successive discounts.

### Step 1: Identify the discounts
Here, both discounts are 10%. So, we have:
- \( x = 10 \)
- \( y = 10 \)

### Step 2: Substitute the values into the formula
Now, we substitute \( x \) and \( y \) into the formula:

\[ \text{Single Equivalent Discount} = 10 + 10 - \frac{10 \times 10}{100} \]

### Step 3: Calculate the product of the discounts
Calculate \( \frac{10 \times 10}{100} \):

\[ \frac{10 \times 10}{100} = \frac{100}{100} = 1 \]

### Step 4: Substitute back into the formula
Now, substitute this value back into the formula:

\[ \text{Single Equivalent Discount} = 10 + 10 - 1 \]

### Step 5: Perform the addition and subtraction
Now, perform the addition and subtraction:

\[ 10 + 10 = 20 \]
\[ 20 - 1 = 19 \]

### Final Answer
Thus, the single equivalent discount is:

\[ \text{Single Equivalent Discount} = 19\% \]